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A log-exponential regularization method for a mathematical program with general vertical complementarity constraints

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  • Based on the log-exponential function, a regularization method is proposed for solving a mathematical program with general vertical complementarity constraints (MPVCC) considered by Scheel and Scholtes (Math. Oper. Res. 25: 1-22, 2000). With some known smoothing properties of the log-exponential function, a difficult MPVCC is reformulated as a smooth nonlinear programming problem, which becomes solvable by using available nonlinear optimization software. Detailed convergence analysis of this method is investigated and the results obtained generalize conclusions in Yin and Zhang (Math. Meth. Oper. Res. 64: 255-269, 2006). An example of Stackelberg game is illustrated to show the application of this method.
    Mathematics Subject Classification: Primary: 90C30; Secondary: 90C46, 90C47.

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